Unambiguous assignment of 13 C NMR signals in epimeric 4,5-epoxy-3-oxo-steroids assisted by X-ray diffraction and gauge invariant atomic orbitals calculation of absolute isotropic shieldings

Complete assignments of the 13 C signals of diastereomeric 4,5-epoxy-3-oxo steroids based on a combination of 1D and 2D NMR techniques are described The assignments were corroborated or corrected by calculation of the absolute isotropic 13 C NMR shieldings using the Gauge Invariant Atomic Orbitals (GIAO) method at B3LYP/6-31+G(d,p) level.


Introduction
Steroids play different roles in living organisms from both animal and vegetal kingdoms.In a wide variety of steroids, the coexistence of different functionality in the steroidal nucleus confers several properties that are interesting from both the biological and the synthetic points of view.][3][4][5] 4,5-Epoxy-3-oxo-steroids can be prepared in moderate to good yield and varying diastereoselectivity by treatment with different reagents that include peracids, 4 H2O2 in alkaline media, 5 dioxiranes 6 and more recently magnesium bis(monoperoxyphthalate) hexahydrate. 7In spite that such compounds have been extensively employed as synthetic precursors for different polyfunctional or rearranged steroids, no complete and unambiguous assignment of the 13 C NMR signals of such compounds is available.This may obey to the fact that in most of the synthetic applications, 4,5-epoxy-3-oxo-steroids have been employed as diastereomeric mixtures, regardless that the different reactivity profile of each diastereomer may affect (or not) the yield.
As a part of our ongoing program on the synthesis of potentially bioactive steroids, [8][9][10][11] we require the unambiguous NMR characterization several pairs of epimeric epoxides derived from different 4-en-3-oxo-steroids that are being employed as synthetic precursors.Herein we report on the unambiguous 13 C NMR assignments of series of epimeric 4,5-epoxy-3-oxo-steroids, assisted by X-ray diffraction and Gauge Invariant Atomic Orbitals Calculation of Absolute Isotropic Shieldings.

Results and Discussion
Treatment of methanol solutions of the 4-en-3-oxo-steroids 1-3 with H2O2 and NaOH produced mixtures of the corresponding  and -epoxides.In the case of testosterone acetate (1) the epoxidation was accompanied with the partial saponification of the acetate at C-17 that was reacetylated by treatment with acetic anhydride in pyridine (see Scheme 1).The diastereomeric relation in each epoxide pair was calculated by relative integration of the 1 H NMR signals corresponding to H-4 in the crude mixtures.Scheme 1. Epoxidation of 4-en-3-oxo-steroids.Accordingly, the 1 H NMR spectra of the -epoxide 1a and its -partner 1b are characterized by the presence of the signals H-4 that appear at 3.02 and 2.96 ppm respectively.The signals of H-19, that appear at 1.05 ppm for the -epoxide 1a and at 1.14 ppm for the -epimer, also characterize the spectra of the epoxidated compounds.These criteria, that was extended to the diastereomeric pairs 2a/b and 3a/b, can be generalized for the fast differentiation and quantification of each component in diastereomeric mixtures of 4,5-epoxy-3-oxo steroids (see Table 1 and Figure 2).

C NMR Analysis Computational studies
With the crystalline structures of epoxide 1a and 1b in hand, the 13 C NMR spectra such compounds were simulated in order to assist, confirm or correct the assignments of the NMR signals.Even though the employed computational code allows obtaining absolute chemical shifts, the values are reported as relative to TMS to facilitate comparisons with the experimental data.
Relative chemical shifts (δc) were estimated by using the corresponding tetramethylsilane (TMS) shielding calculated as: In addition, the δc values were improved by using the procedure suggested by Forsyth and Seabag. 12It consists on scaling the theoretical shielding values using the slope (a) and intercept (b) obtained from a linear regression analysis of experimental chemical shifts and the calculated dr =1 /3.92 shieldings.It should be noted that the values of parameters a and b are generally method-and basis-set dependent, but the a value is expected to be close to 1.This procedure has been successfully employed, [13][14][15][16] and is currently accepted as a reliable way of improving NMR data obtained from calculations.In the present study the correlation σc vs. δ exp has been used for that purpose, and thus the scaled values correspond to: The calculated 13 C isotropic chemical shielding of TMS was found to be 193.6 ppm, i.e. 5.5 ppm larger than the experimental value is (188.1 ppm). 17Since it is a significant deviation, to calculate the relative 13 C chemical shifts of epoxides 1a and 1b, two different approaches were employed.The first one is to use the computed absolute shift of TMS as reference in the calculation of the relative values to obtain δc (Equation 1), and the other one to use the Forsyth and Seabag procedure 12 to obtain scaled values of the chemical shifts (δc scal , Equation 2) The linear correlations for the latter case are shown in Figure 3.The slope in both cases is ≈ -1 and the correlation coefficients (R 2 ) values are ≈ 1, which supports the reliability of the calculated 13 C NMR data.In addition, this value simplifies the form of Equation 2, leading to a scaling procedure consisting only on adjustments based on subtraction from a fixed reference.Accordingly, the expressions used to calculate the δc scal values for epoxides 1a and 1b are: δc scal (1a) = 189.02-σc (1a) (3) δc scal (1b) = 189.24-σc (1b) (4) It is interesting to notice that the b values obtained from the correlations are very similar for epoxides 1a and 1b (189.02 and 189.24 ppm, respectively), supporting the consistency of the calculations at the given level of theory.
The calculated values are listed in Table 2, together with the deviations from the experimental values and the corresponding mean unsigned errors (MUE).It was found that the non-scaled chemical shifts (δc, Equation 1) lead to Mean Unsigned Errors (MUE) values of 4.3 and 4.2 ppm, for epoxides 1a and 1b, respectively.The agreement between the calculated and the experimental data is significantly improved when the scaling procedure is used (δc scal , Equations 3 and 4), leading to MUE values equal to 1.1 ppm for both epoxides 1a and 1b.It should be noted, however, that the trend of the calculated signals is the same regardless the procedure used to calculate the chemical shifts.

C NMR signals assignments and shielding effects
The chemical shifts associated to the C/D rings and the side chains of are in good agreement with the previously available shielding data. 18Assignments of the signals corresponding to the A/B rings in compounds 2a/b and 3a/b are in good agreement with the data obtained above for compounds 1a/b (see Table 3).The fact that, regardless the differences in the side chains, similar shielding profiles are observed amongst the  or -epoxides, accounts for the accuracy of both, the theoretical and experimental assignments.
Comparison of the NMR spectra of each / pair shows that the resonance signal of C-9 in the -epoxides is shifted -4.2 ppm respect to that of the -counterpart.Electronic compression of H-9 exerted by the C-2 methylene may justify this effect that is only present in the -epoxides.A similar, but lower (-2.9 ppm) upfield shift is observed in the -epoxides when their C-1 signals are compared with those of the -partner and can be interpreted as the result of an O↔H-1 interaction that in the -epoxides compress H-1and results in the shielding of C-1.
Downfield shifts in the signals of C-7 and C-19 of the -epoxide are observed when compared to those of the -partner.In the case of C-19, the observed effect may be interpreted as the result of the absence of the -syn H-2↔H-19 interaction that in the -epoxides shields C-19.Downfield shift of the signal of C-7 in the -epoxides may be considered a consequence of the absence the O↔H-7 syn interaction that in the -epoxides shields C-7 (see Table 3 and Figure 4).In molecule B the O-3 of the 17β-acetoxy shows disorder in two positions (O-3b and O-3p) with 70:30 of O-3b:O-3p occupancy respectively.In order to establish differences among the studied molecules A and B of compound 1b, a least-squares overlay analysis of the structures by pairs was performed.Table 4 shows the results obtained with the Mercury program. 24Small differences are observed in the A ring (rms 0.0672) and in the torsion angles of 170.64 and 177.58° of the 17β-acetoxy group respectively bonded to C-17a and C-17b (notice that the observed deviations in rings A to D are less than 0.0673).

Conclusion
The generalized practice for the determination of orientation of substituents in the steroid framework by observation of NOE effects, fails in the case of 4,5-epoxy-3-oxo steroids.After the unambiguous identification of the  and -diastereomers by X-ray studies, a fast and reliable criteria, based on the chemical shifts of H-4 and H-19 of each diastereomer, allows both the identification and quantification of each component in the crude reaction mixtures.
Complete and unambiguous assignments of the 13 C signals of the studied compounds based on a combination of 1D and 2D NMR techniques was assisted by calculation of absolute isotropic 13 C NMR shieldings using the Gauge.The agreement between the experimental assignment and theoretical results accounts for the accuracy of both, the experimental and theoretical data.

X-ray crystal structure determination
Suitable crystals for X-Ray diffraction studies were obtained by slow evaporation of the ethyl acetate solutions of epoxides 1a and 1b at room temperature.Crystals of compounds 1a and 1b mounted on glass fiber were studied with Oxford Diffraction Gemini "A" diffractometer with a CCD area detector (MoK = 0.71073 Å, monochromator: graphite) source equipped with a sealed tube X-ray source at 130 K. Unit cell constants were determined with a set of 15/3 narrow frame/runs (1° in ) scans.A data sets consisted of 133 and 183 frames of intensity data collected for the epoxides 1a and 1b respectively with a frame width of 1° in , a counting time of 10 s/frame, and a crystal-to-detector distance of 55.00 mm.The double pass method of scanning was employed to exclude any noise.The collected frames were integrated by using an orientation matrix determined from the narrow frame scans.Crystallographic data have been deposited with the Cambridge Crystallographic Data Center as supplementary material numbers CCDC 899268 (compound 1a) and CCDC 899269 (compound 1b).Copies of the data can be obtained free of charge on application to CCDC, 12 Union Road, Cambridge CB2 1EZ, UK. fax: +44(0)1223-336033; email: deposit@ccdc.cam.ac.uk, or from www.ccdc.cam.ac.uk/conts/retrieving.html.CrysAlisPro and CrysAlis RED software packages 25 were employed for collection and integration of data.Analysis of the integrated data did not reveal any decay.Final cell constants were determined by a global refinement of 5818 and 8298 reflections ( < 26.3 °) for 1a and 1b respectively.Collected data were corrected for absorbance by using analytical numeric absorption correction 26 using a multifaceted crystal model based on expressions upon the Laue symmetry employing equivalent reflections.Structure solution and refinement were carried out with the programs SHELXS97 and SHELXL97. 27Molecular graphics were generated with ORTEP-3 for Windows and software employed for preparation of the material for publication was WinGX. 28ull-matrix least-squares refinement was carried out by minimizing (Fo 2 -Fc 2 ) 2 .All nonhydrogen atoms were refined anisotropically.Hydrogens attached to carbon atoms were placed in geometrically idealized positions and refined employing the riding model, with C-H distances = 0.98 -1.00 Å with Uiso (H) = 1.2Ueq(C) for methylene and methyne groups, and Uiso (H) = 1.5 Ueq(C) for methyl group.Crystal data and experimental details of the structure refinement are summarized in Table 7.
Computational details.Geometry optimizations and frequency calculations were performed using the B3LYP functional and the 6-31+G(d,p) basis set.They were carried out in solution, using the SMD continuum model 29 and chloroform as solvent.Geometries were fully optimized without imposing any restriction, using the X-ray structures as starting points.Local minima were confirmed by the absence of imaginary frequencies.All the electronic calculations were performed with Gaussian 09 package of programs. 30After optimization, the absolute isotropic 13 C NMR shieldings (σc) were calculated using the GIAO (Gauge Invariant Atomic Orbitals) method 31,32 in chloroform also at B3LYP/6-31+G(d,p) level.

Figure 4 .Figure 5 .
Figure 4. Molecular models of the epoxides 1a and 1b generated from the crystal data (distances in Å)

Figure 6 .
Figure 6.ORTEP drawing of the asymmetric unit of epoxide 1b showing molecules A and B with the thermal ellipsoids drawn at the 50% of probability.

Figure 7 .
Figure 7. Crystal structure of epoxide 1b viewed along the b axis, showing the short contacts between the symmetry equivalent for molecule A (green) and molecule B (blue) extending along the c-b plane.

Table 1 .
NMR signals of H-4 and H-19 in each pair of epoxides 1a/b, 2a/b and 3a/b

Table 3 .
Assignments of the 13 C NMR experimental signals of the studied pairs of diastereomeric epoxides 1a/b, 2a/b and 3a/b ( ppm)

Table 4 .
Least-square overlay analysis for each pair of molecules A and B of compound 1b

Table 5 .
Crystal data and structure refinement parameters for epoxides 1a and 1b